No, you don't need a transit visa - as long as you don't leave the transit lounge. But be sure about your change with airlines/planes, as there are two airports in Istanbul. You may read detailed information on the Turkish Ministry of Foreign Affairs website.
Edit (not by Mahmut) to include extract from part of the referenced website:
Question: I will be flying to Europe. I know that our aircraft will land in İstanbul. I am not planning to leave the transit lounge. Do I need to get transit visa?
Answer: If you will not leave the transit lounge at the airport you are not required to have transit visa.
The above to attempt to clarify that in the above circumstances the nationality of the traveller appears irrelevant (though so does "I will be flying to Europe", and interlining of luggage is not covered by the extract).